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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
58% (02:03) correct
42%
(01:58)
wrong
based on 509
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There are 210 households in a certain residential complex. All households in the complex that have more than one dog also have at least one cat. All households that have at least one cat have a pet rodent. How many households in the complex have a pet rodent?
(1) 18 households in the complex have two or more dogs.
(2) 90% of households in the complex that have a pet rodent have at least one cat.
(1) 18 households in the complex have two or more dogs.
(2) 90% of households in the complex that have a pet rodent have at least one cat.
16 Nov 2023, 12:57
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There are 210 households in a certain residential complex. All households in the complex that have more than one dog also have at least one cat. All households that have at least one cat have a pet rodent. How many households in the complex have a pet rodent?
(1) 18 households in the complex have two or more dogs.
(2) 90% of households in the complex that have a pet rodent have at least one cat.
(1) 18 households in the complex have two or more dogs.
(2) 90% of households in the complex that have a pet rodent have at least one cat.
A good CR-type question!
Statement 1
(1) 18 households in the complex have two or more dogs.
Based on the given information, we can deduce that a minimum of 18 households within the complex possess rodents as pets. This conclusion is drawn from Statement 1, which specifies that 18 households in the complex own two or more dogs. Additionally, considering the initial question premise, it is established that every household in the complex with multiple dogs also harbors at least one cat, and each household with a cat possesses a pet rodent. Consequently, we can affirm that the complex comprises a minimum of 18 households that own pet rodents.
However, we cannot conclude that ONLY 18 households have a pet rodent. The complex may include households with solely pet rodents or those with a combination of a pet rodent and one dog. Therefore, the statement alone is insufficient to definitively answer the question, leading us to eliminate options A and D.
Statement 2
(2) 90% of households in the complex that have a pet rodent have at least one cat
This statement furnishes details regarding households that possess a pet rodent, explicitly stating that all such households also possess a cat. Nevertheless, the initial information about the total number of households with a pet rodent is absent. Without this essential data, we lack the necessary foundation to find answers to the question asked. Therefore, this statement is insufficient.
Combined
The combined statements fail to provide a conclusive answer as they do not eliminate the possibility that a household might exclusively have a rodent as a pet or could have another animal in addition to a rodent. The ambiguity persists, preventing us from definitively determining the composition of households with pet rodents.
Hence, Option E
General Discussion
16 Nov 2023, 13:15
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I think the answer is E, both options are insufficient.
From the argument, we know that:
- (household has > 1 dog) = (household has >= 1 cat)
- (household has >= 1 cat) = (household has >= 1 rodent)
Question: how many households have a rodent
Option 1
18 households have 2 or more dogs i.e 18 households have > 1 dog
18 households with > 1 dog = 18 households with >= 1 cat
But what about all the households with cats but no dog or just one dog? They are not reflected in the 18 households mentioned above.
Therefore it is more accurate to say that:
(18 households with > 1 dog) = (18 or more households with >= 1 cat)
(18 or more households with >= 1 cat) = (18 or more households with rodents)
18 or more can be 18, 19, 29, 49....
Because we don't have one distinct possible answer, this option is insufficient
Option 2
90% of households in the complex that have a pet rodent have at least one cat
You can't calculate anything from this. Clearly insufficient.
Together
Combining doesn't really add any new information to make this question solvable
From the argument, we know that:
- (household has > 1 dog) = (household has >= 1 cat)
- (household has >= 1 cat) = (household has >= 1 rodent)
Question: how many households have a rodent
Option 1
18 households have 2 or more dogs i.e 18 households have > 1 dog
18 households with > 1 dog = 18 households with >= 1 cat
But what about all the households with cats but no dog or just one dog? They are not reflected in the 18 households mentioned above.
Therefore it is more accurate to say that:
(18 households with > 1 dog) = (18 or more households with >= 1 cat)
(18 or more households with >= 1 cat) = (18 or more households with rodents)
18 or more can be 18, 19, 29, 49....
Because we don't have one distinct possible answer, this option is insufficient
Option 2
90% of households in the complex that have a pet rodent have at least one cat
You can't calculate anything from this. Clearly insufficient.
Together
Combining doesn't really add any new information to make this question solvable
